Name______________________________
Date: _________________ Block:_______
Ms. Gallagher
Warm – Up
1. Evaluate the function for the indicated values f(x) = 3x – 2
a. f(2) =
b. f(0) =
c. f( -2) =
2. Graph the two linear equations on the same x-y plane below
y = –x – 4
y = 2x + 1
Notes Piecewise Functions
If we want a function to behave differently depending on the x- values, we
need a piecewise function. A piecewise function is just a function that uses
more than one equation to describe its behavior. When we graph
piecewise functions, we are really graphing different pieces of different
lines.
Example One Evaluating a piecewise function
f ( x)
a) f(1)
2x
1
x
3
5, x
2
1, x
2
b) f(2)
f ( x)
a) f(-6)
x
c)
x2 , x
4
2, x
4
b) f( -4)
f(3)
c) f( -2)
Example Two Graphing a piecewise function using a table of values
f ( x)
2x
x
1,
3,
x
x
1
1
Steps:
1)
2)
3)
4)
Example Three Graphing a piecewise function using a switch point
f ( x)
2x
x
1,
3,
x
x
1
1
Steps:
1)
2)
3)
4)
Example Four Writing a piecewise function
Example Five Word Problem
You have a summer job that pays time and a half for overtime. (If you work more
than 40 hours) After that it is 1.5 times your hourly rate of $8.00/hr. Write a
piecewise function that models your pay schedule and graph the function.
Example Six Graph the Step Function
f ( x)
1,
2,
3,
6
3
0
x
x
x
0
3
4,
3
x
6
Homework
Worksheet
3